Measuring the gas pressure drop relative to time (pressure rate of decay) in a known volume (control volume) is one method to calculate gas flow rate. Such a method is normally only used in calibration systems, where strict control of ambient conditions is possible, and where there is sufficient time allowed in the pressure drop operation (blowdown) to allow the gas to reach ambient temperature. The article “Two Primary Methods of Proving Gas Flow Meters” by B. T. Arnberg, Symposium on Flow: Its Measurement and Control in Science and Industry, Paper Number 3-8-216, 1971, states that this method is designed to provide the high accuracy required for calibration of transfer standards, but is too time consuming to be practiced for the routine calibration of flow meters. Arnberg notes that during a measurement test at least an hour was allowed for thermal equilibrium to be established before pressure and temperature measurements were made.
U.S. Pat. No. 5,925,829 to Laragione et al. discloses a method and apparatus for determining a rate of flow of gas by a rate of change of pressure. The method and apparatus are disclosed as being useful in the manufacture of mass flow controllers and mass flow meters to calibrate them. A gas container used as a control volume in the method and apparatus is maintained in a substantially isothermal or temperature invariant condition and means are provided within the container for maintaining the gas in isothermal relationship with the surroundings of the container. During the method, the container temperature is sensed and if temperature changes of greater than 0.01° C. per second are detected, the system waits during which time no gas is flowed. The sensed container temperature is used in the calculations to determine actual flow rate.
Gas temperatures in the control volume during these methods to calculate flow rate are affected by the nature of the gas expansion. As gas is removed from the control volume during the measurement process, the remaining gas expands. This causes the remaining gas to cool in a process referred to as adiabatic expansion. A process that is 100% adiabatic would indicate that there is no heat transfer to the gas during the pressure drop. A process that is 0% adiabatic would indicate that the gas temperature remains constant. This is referred to as isothermal expansion. In reality, in the aforementioned conventional methods and apparatus the gas expansion will typically be partially adiabatic, resulting in some temperature change during the blowdown process. The degree to which the process is isothermal is dependent on several factors, including: flow rate, temperature, temperature stabilization time, Reynolds number, and specific gas thermal characteristics.
Flow controllers for delivering gas used in production facilities, such as those used in delivering process gas in the fabrication of semiconductors, do not have the luxury of operating at standard pressure and temperature. It is often necessary to heat the flow controller to prevent condensation of a process gas. Process run times can be as short as several seconds, so that if a blowdown operation is to be performed during the delivery of a batch of process gas, then the blowdown operation must be very fast, on the order of one second or even shorter. There is no time at the end of the blowdown operation to allow the control volume to sit in a static condition in order to allow the control volume gas to reach ambient temperature as in the aforementioned known methods and apparatus.
Assignee's U.S. Pat. Nos. 6,363,958 B1 and 6,450,200 B1 disclose flow control of process gas in semiconductor manufacturing wherein measuring pressure drop relative to time in a known volume is performed to calculate flow rate. As disclosed therein, the reference capacity/control volume for the gas incorporates a temperature sensing element to measure the temperature of the gas inside the capacity at the conclusion of the flow verification operation to calculate the flow rate. However, because of the corrosive nature of many of the gases used in semiconductor fabrication, the temperature sensor must be isolated from the process gas. This results in a delay in the response time of the temperature sensor. Consequently, the indicated temperature at the end of the blowdown process will deviate from the actual gas temperature if there is any cooling of the gas due to adiabatic expansion. This will lead to an error in the calculated final molar volume of gas in the known volume and an error in the calculated flow rate which reduces the accuracy of the flow of process gas by the flow control apparatus. There is a need for an improved flow control apparatus and method of measuring gas pressure drop relative to time in a known volume to calculate gas flow rate, for use within a fluid circuit having a source of pressurized gas to be delivered at a controlled flow to a destination which make it possible to calculate the actual flow of gas with a high level of accuracy during the delivery.